analysis / Banach Algebras, Operator Theory

A Unital Banach Algebra That Is Not a Calkin Algebra

The realisation problem asks which unital Banach algebras arise as the Calkin algebra $\mathcal{B}(X)/\mathcal{K}(X)$ of some Banach space. Recorded in Tarbard's thesis and studied by Horváth and Kania. The paper exhibits a unital Banach algebra that cannot be one.

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analysisJul 19, 2026Significance 15/100Registry: unreviewed

A Unital Banach Algebra That Is Not a Calkin Algebra

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The realisation problem asks which unital Banach algebras arise as the Calkin algebra $\mathcal{B}(X)/\mathcal{K}(X)$ of some Banach space. Recorded in Tarbard's thesis and studied by Horváth and Kania. The paper exhibits a unital Banach algebra that cannot be one.

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The realisation problem asks which unital Banach algebras arise as the Calkin algebra $\mathcal{B}(X)/\mathcal{K}(X)$ of some Banach space. Recorded in Tarbard's thesis and studied by Horváth and Kania. The paper exhibits a unital Banach algebra that cannot be one.

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